$\begin{aligned} &A = 7x^2-3x+10 \\\\ &B = -4x^2+6x-4 \end{aligned}$ $A-B=$
Solution: Since we are asked to find $A-B$, let's substitute in the trinomial expressions that we are given for $A$ and $B$ : $A-B = (7x^2-3x+10)-(-4x^2+6x-4)$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(7x^2-3x+10){-}(-4x^2+6x-4)\\ \\ =&(7x^2-3x+10){-}(-4x^2){-}6x{-}(-4)\\ \\ =&7x^2-3x+10+4x^2-6x+4 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${x^2}, {x},$ and the $\text{{constant}}$ term: ${{7x^2} {-3x} {+10} {+4x^2} {-6x} {+4}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(7+4)x^2} + {(-3-6)x} + {(10+4)}}$ When we add the coefficients in front of each term, we get the following trinomial: ${11x^2-9x+14}$